Journal of the Operations Research Society of China ›› 2024, Vol. 12 ›› Issue (2): 505-519.doi: 10.1007/s40305-022-00427-3

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The Q-index and Connectivity of Graphs

Peng-Li Zhang1, Li-Hua Feng2, Wei-Jun Liu2, Xiao-Dong Zhang1   

  1. 1 School of Mathematical Sciences, MOE-LSC, SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240, China;
    2 School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
  • Received:2021-06-20 Revised:2022-04-17 Online:2024-06-30 Published:2024-06-12
  • Contact: Xiao-Dong Zhang, Peng-Li Zhang, Li-Hua Feng, Wei-Jun Liu E-mail:xiaodong@sjtu.edu.cn;zpengli@sjtu.edu.cn;fenglh@163.com;wjliu6210@126.com
  • Supported by:
    Xiao-Dong Zhang is partly supported by the National Natural Science Foundation of China (Nos. 11971311, 12161141003, and 12026230) and Science and Technology Commission of Shanghai Municipality (No. 22JC1403600); Li-Hua Feng and Wei-Jun Liu are partly supported by the National Natural Science Foundation of China (Nos. 11871479, 12071484) and Hunan Provincial Natural Science Foundation (Nos. 2020JJ4675, 2018JJ2479).

Abstract: A connected graph G is said to be k -connected if it has more than k vertices and remains connected whenever fewer than k vertices are deleted. In this paper, for a connected graph G with sufficiently large order, we present a tight sufficient condition for G with fixed minimum degree to be k -connected based on the Q-index. Our result can be viewed as a spectral counterpart of the corresponding Dirac-type condition.

Key words: Q-index, Minimum degree, k-connected

CLC Number: